Ink on Porous Paper or Water Bleed Effect
After messing with settings.

Basics:

To achieve 'ink drop on paper' effect we will be using Fluid System and Dynamic Paint. Fluid gives us nice control over drop shape. Blender units are used in this answer.

Set up:


Plane with dimensions 8x8 - this is our 'paper' - it must be subdivided number of times (higher is better) I'm using 2 Subsfurf modifiers, first set to 6 and second to 2 both set as Simple, they need to be over the Dynamic Paint modifier.
Sphere (16 segments, 8 rings, 0.3 size), moved by 3 units over Z axis (G > Z > 3) - this is our drop.
With selected Sphere hit Space search for Quick Fluid and apply.
Select Domain and Scale/Position it to cover whole plane.




Fluid:


Select 'paper' (plane) and in Properties tab choose Physics then select Fluid and set Type to Obstacle. Decrease Slip Type Amount to 0.1
Select Domain and under Fluid World > Viscosity Presets set Base to 2 and Exponent to 3. Under Fluid Boundry set Slip Type > Amount to 0.03


Exponent is very important here, if you want to preserve shape of your fluid you will need to set it to 0, and if you want to have random splatter set it higher.

Another important thing in Fluid Domain is Resolution, we will be using here 65 for preview but higher will give much better results

Dynamic Paint:

Brush


With selected Domain add Dynamic Paint (Physics tab).
Set Dynamic Paint to Brush and then Add Brush.
Change color if you want.
Under Dynamic Paint Source set Paint Source to Proximity, Falloff to Color Ramp and set Color Ramp as in the picture below:




Canvas


Select our 'paper' (plane) go to Physics tab and add Dynamic Paint > Canvas > Add Canvas.
Under Dynamic Paint Advanced set Dry Time to 25.
Under Dynamic Paint Initial Color choose Color and set it as you like.
Under Dynamic Paint Effects check Use Spread and set it to 0.5 then go to Drip and check it as well (it will give us control over the splatter by force fields).




Force field:


Add Force Field > Turbulence and set it to Strenght 10 and Flow 1.
Bake your fluid and play animation.



Domain and Fluid are hidden here.


Fluid resolution - 128 and some other sligt changes. This is from .blend file.

Final thoughts:

There are many things to play with in order to get higher resolution/better looking effect as I mentioned it above. Fluid resolution, mesh (paper) subdivision, substeps in Canvas. You could change Influance Scale and Radius Scale under Canvas > Dynamic Paint Advanced to have 'lighter look' of ink. It's all up to you. Now when you know the method it will be fun to mess with it.

Blend file: